The concept of the heat pipe was first introduced by Gaugler in 1942 (c$

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1 LITERATURE REVIEW C. Muraleedharan Heat transfer and fluid flow studies on flat heat pipe Thesis. Department of Mechanical Engineering, Calicut Regional Engineering College, University of Calicut, 2001

2 Chapter 2 LITERATURE REVIEW 2.1 Introduction The concept of the heat pipe was first introduced by Gaugler in 1942 (c$ Dunn and Reay, 1982). According to Gaugler, the objective of his invention was "to cause absorption of heat, or in other words evaporation of the liquid to a point above the place where the condensation or giving off heat takes place without expending upon the liquid any additional work to lift the liquid to an elevation above the point at which condensation takes place". A capillary structure was proposed as the means for returning the liquid from the condenser to the evaporator. However, it was not widely publicised until 1963 when Grover (c$ Dunn and Reay, 1982) reinvented the concept. Grover demonstrated it as a high performance heat transmission device, named it "The Heat Pipe" and developed its application at Loss-Alamos Laboratory, New Mexico. After Grover's publication, extensive work on heat pipe was carried out at UK Atomic Energy Laboratory in Harwell and at ISPRA in Italy. The areas of application of the heat pipe extended from thermionic emitters and refrigeration purposes to satellite cooling, air conditioning, cooling of electronic components, engine cooling, etc. Several types of wick structures were proposed and many working fluids were used. Along with the conventional heat pipes increasing interests are also found now

3 a days in the area of flat rectangular heat pipes, disk type heat pipes, rotating heat pipes, flexible heat pipes and micro heat pipes. 2.2 Literature Review Large number of theoretical and experimental investigations have been carried out with heat pipes and the reports are available in literature. The majority of the publications are on the flow of working fluid that too in the vapour core and heat transfer in cylindrical heat pipes. Some literature are also available on the flow of liquid through the capillary wick structure. Researchers and experimenters have recently started showing interest in the combined analysis of vapour core and liquid wick regions of the heat pipe. This chapter gives an overview of the important literature available on the heat pipes. Both the works done on cylindrical heat pipes as well as on flat heat pipes are reviewed here Cylindrical Heat Pipes Traditionally, heat pipes are cylindrical in shape. Hence, majority of the investigations are done in the area of circular heat pipe. The working principle, the fluid flow and heat transfer mechanism are similar in any heat pipe (irrespective of the shape). Therefore the review of the works on cylindrical heat pipes is done here with respect to fluid flow and heat transfer mechanism in a heat pipe. In the field of circular heat pipes the contribution of Busse is invaluable. Under the leadership of Busse, ISPRA, Italy had become the focal point of heat pipe activities in Europe. Busse first analysed (1967, 1970 and 1973) the problem of pressure drop in laminar vapour flow in a long cylindrical heat pipe. Poiseuille

4 velocity profile was assumed. The analysis leads to similarity 'profiles for the evaporation zone and variation of profiles with the axial distance in the condenser zone. Busse et al. (1 970) have developed high temperature cylindrical heat pipes for thermionic converters. Niobium, Zirconium and Tungsten were the container materials used. The working substances used were Lithium, Lead, Bismuth and Barium. The temperature range selected was between 1500 C and 2000 C for the operation of their heat pipes. Busse (1973) presented the ultimate limit of heat transfer for the cylindrical heat pipes with laminar vapour flow. The heat transfer in the heat pipe is limited either by insufficient return flow of condensate or by vapour flow limitation. Busse has proved that, if the return flow is guaranteed by a suitable wick, the heat flux is ultimately limited by vapour flow effects only. He described the two different regimes of vapour flow as inertia flow regime and viscous flow regime. Busse predicted approximate expressions to compute these heat transfer limits. His analysis shows that, the ultimate limit of heat transfer is of the viscous type below a certain temperature. Busse (1980 and 1982) have reported about the analysis of dryout mechanism in gravity-assisted cylindrical heat pipes with capillary flow. Busse and Loehrke (1989) have presented further a method for the prediction of laminar subsonic flow in cylindrical heat pipes. They have described about the velocity profiles, including strong flow reversals occurring within the heat pipe. The calculation of pressure recovery at the condenser section was also reported by them. Chun (1972) carried out an experiment to predict the dry out limits on screen wick. A new model was proposed by him for the wick dry out. Chun found that his model predicts with in 10 percent of the experimental dry out heat inputs which are

5 below the values that would be expected if the evaporator wick were fully saturated with liquid. Tien and Rohani (1972) have established a theoretical frame work for predicting the steady state operational characteristics of a two component heat pipe. They showed the variation of temperature and pressure along the heat pipe by applying the law of conservation of mass and energy as well as thermodynamic equilibrium relations. In order to substantiate the validity of the theoretical model, a series of experiments were carried out on a horizontal cylindrical heat pipe with water and ethanol mixture as the working fluid. Tien and Rohani (1974) have also studied the effects of vapour pressure drop on vapour temperature, evaporation and condensation rates on a cylindrical heat pipe. Stream function-vorticity approach was used to solve the two dimensional axisymmetric problem. In addition, they introduced the energy conservation equations and thermodynamic equilibrium equations to couple the vapour pressure and the temperature. Variation of temperature and pressure were presented up to a radial Reynolds number of 36. Bankston and Smith (1973) reported the two dimensional analysis of a cylindrical heat pipe. For laminar flow the mass and momentum equations are solved with finite difference computational method based on stream function vorticity approach, thus eliminating pressure as a separate variable. The results are reported over a wide range of Reynolds number (Re) values, from very small to very high. For different ranges of Re values, the convergence and accuracy of the method depended largely on the appropriate choice of the vorticity boundary conditions. In each particular range of increasing Re values deviations from Poiseuille flow become evident first in the condenser. Flow reversal is encountered for Re values greater than 2.

6 Faghri and his co-workers have done a lot of research work on heat pipes. Faghri and Thomas (1989) fabricated and tested successfully a newly designed concentric annular heat pipe. They carried out theoretical and experimental studies to predict the capillary limit on concentric annular heat pipe. A significant increase of the heat capacity per unit area was found compared to conventional circular heat pipes. Cao and Faghri (1990) have studied the phase change mechanisms in the heat pipe, numerically. They have presented the two dimensional model for compressible flow analysis with respect to high temperature cylindrical heat pipes also. A numerical model was presented by Chen and Faghri (1990) for the overall performance of the cylindrical heat pipes with single or multiple heat sources. The analysis includes the heat conduction through wall and liquid wick regions considering the compressibility effect of the vapour inside the heat pipe. The two dimensional governing equation and thermodynamic equilibrium relations with appropriate boundary conditions are solved. The axial temperature and pressure obtained and compared with the existing experimental results. Faghri and Buchko (1991) carried out experimental and numerical analyses of the effects of heat load distribution on the vapour temperature, wall temperature and heat transfer capacity for heat pipes with multiple heat sources. An optimization of heat distribution of such heat pipes was performed and found that the heat capacity can be increased by redistribution of heat loads. Jang and Faghri (1991) have reported a one dimensional transient analysis on cylindrical heat pipe, treating the vapour as compressible using an implicit finite difference scheme. In addition to the pressure variation with respect to time, velocity and temperature distribution against axial distance at steady state conditions have also

7 been obtained. Faghri and Harley (1994) have described two dimensional models of conventional circular and gas loaded heat pipes. In both the cases the axial conduction through the wall was incorporated in the analysis. By lumped analysis of conventional heat pipe, they have obtained the temperature distribution at transient and steady state conditions. Comparison of numerical solutions with the experimental data was also given. The mathematical model detailed by Khrustalev and Faghri (1995) describes the heat transfer through liquid films in the evaporator of.heat pipe with capillary grooves. The model accounts for the effects of interfacial thermal resistance, pressure and surface roughness for a particular contact angle. The free surface temperature was determined and the expression for interfacial resistance was given by kinetic theory. Shibayama and Morooka (1979) have studied the evaporation mechanism within the evaporator of the heat pipe. They evaluated the effects of working pressure, working substance, heat pipe inclination and production of non condensable gases. Water and F 1 13 were the working fluids used. Heat transfer coefficients were obtained from the experimental analysis. They have also worked to determine the operating limits of heat pipes (1980). The experimental analysis was on wick characteristics corresponding to maximum heat transfer rates. Sintered metallic powder was used as wick along with working substances water and F1 13. They have studied the wick characteristics, friction losses in the heat pipe and capillary properties. A simplified model was also developed to predict the maximum heat transfer for capillary limits. Maximum heat flux in the heat pipe was measured and presented.

8 The natural convention in vertical porous cylinder with uniform heat generation and side wall cooling was reported by Rao and Wang (1991). Their analysis was using partial Galerkin method and finite difference method. The stream lines, isotherms and vertical velocity profiles were obtained. The objective of another investigation by Issacci (1991) was to find the dynamic behaviour of the vapour flow in heat pipes during its start-up phase. The complex vapour flow was analysed using a two dimensional model treating it as compressible flow in an enclosure with inflow and outflow boundary conditions. Using the implicit finite difference method, the heat flux development and variation of temperature, pressure and velocity of flow were discussed. A one dimensional model of the vapour flow in heat pipe which is different from previous models was reported by Bowman and Beran (1993). The vapour flow was assumed to be incompressible with space even though compressibility with 9 respect to time is considered. The vapour densities predicted by them indicates that ideal gas behaviour can deviate greatly from saturated vapour densities. El-Genk and Huang (1993) studied the transient response of water heat pipe at different heating rates. Mainly the temperature distribution along the heat pipe, viz. in the vapour core and through the wall, was studied. A cylindrical heat pipe made of copper with copper wire screen of mesh number 150 was used for their experiment. Tournier and El-Genk (1994) have presented the results of two dimensional transient heat pipe model and the experiment conducted on a cylindrical copper heat pipe using water as the working fluid. The outcome of the work includes the transient and steady state characteristics of vapour flow and liquid flow and variation of temperature and pressure in the heat pipe. They have found out the axial distribution

9 of vapour and liquid pressure. The analysis of start up of sodium heat pipe from frozen state has also been presented by them in another paper (1996). The calculated temperature at different times during st& up are found in good agreement with the measured values. Hsiao et al. (1994) have analysed numerically the steady state convection in an inclined porous cavity with a discrete heat source on a wall. Non-Darcy and thermal dispersion effects are considered in the momentum and energy equations. Wall effects on porosity, permeability and thermal dispersion are also taken into account. The numerical solution procedue employed was finite difference method on stream function - vorticity approach. Imura et al. (1994) conducted extensive experimentation on screen wick to find out the effective pore radius. The capillarity of stainless steel and phospher bronze screen mesh was measured with water, ethyl alcohol and F 113 as test liquids. The experimental data showed that the contact angle of the liquids are much different from the values that were assumed. An expression for the capillary pressure was also presented in their paper. Sun et al. (1995) proposed an approximate method to calculate the effective length of a flat heat pipe when the strip heater is partially covering the evaporator section. They found that a higher capillary transport limit can be achieved, if the heat source is placed symmetrically at the centre of the evaporator section. Evaporative heat transfer at the evaporator section of grooved heat pipe has been presented by Khrustalev and Faghri (1995) and Kobayashi et al. (1996). Numerical results presented by the latter indicate that a large heat flux of the order of MWIm is transported in the narrow micro region which is close in contact to the solid wall. Kobayashi et al. (1996) investigated the evaporative heat and mass transfer

10 phenomena at the liquid meniscus edge in the evaporator of a grooved heat pipe. They proposed an analytical model to simulate this phenomena. Numerical results were obtained for ammonia as the heat pipe liquid. Optical measurement was conducted at the meniscus edge to confirm the existence of the non-evaporative liquid l film and to identify the thickness in the order of few nanometres. Hall and Doster (1990) have presented a transient model for liquid metal heat pipes. Their contribution is the calculation of evaporation and condensation accommodation coefficients. Abhat and Seban (1974) studied the heat transfer mechanism by boiling and evaporation from the wicks with water and acetone as working substances. Bairamov and Toiliev (1981) used the diode property of the heat pipe in the application in solar collectors. Bilegan and Fetcu (1 981) conducted study on heat pipe with axially grooved wicks. They have reported that using the inexpensive axial grooves for the wick structure, high heat transfer rates can be achieved. The working substance used was R12. The performance has been studied with various parameters like operating temperature, heat pipe inclination and length of the heat pipe. Bilegan and Fetcu (1981) concluded that the heat pipe can be effectively used in waste heat recovery systems. Very few investigators have studied the effect of the amount of working fluid on the performance of heat pipe. Larkin (1981) has presented one of the early reports which explains about the effect of fluid quantity in the heat pipe. He has studied the performance of heat pipe in a compact air-to-air heat exchanger. R22 was used as the working fluid in his studies. Temperature profiles, pressure and heat transfer coefficients in the heat pipe were obtained. Peretz (1981) also have studied the heat transfer effectiveness of a heat pipe exchanger using NTU method.

11 Thermodynamic analysis of heat pipe has been done by Vasiliev and Konev (198 l), Richter and Gottschlich (1994) and Zuo and Faghri (1998). Vasiliev and Konev (1981) analysed the heat transfer for dry, moist and superheated vapour as well as in the subcooled fluid phase. Richter and Gottschlich (1994) showed an approach to the general operation and performance of heat pipes from fundamental thermodynamic considerations. In contrast with the classic heat pipe theory in which the circulation of the working fluid occurs due to the capillary pumping pressure and the pressure difference of vapour and liquid working medium, an attempt has been made to analyse this by conversion of thermal energy into kinetic energy. Zuo and Faghri (1998) also provided a unique view into the physics behind the heat pipe operation which was considered as a thermal network of various components. Many investigations have been reported on the compatibility of materials used for the wick and working substance. Acton (1981) studied the flow and heat transfer through metal felt in the heat pipe. Experimentally, he has predicted the effective thermal conductivity, capillary radius and permeability of the sintered metal felt wick of, copper, nickel and stainless steel. Feldman and Kenney (1981), Munzel and Krahling (1981), and Petrick (1993) investigated the heat pipe mechanism with ferrous metal wicks when water is used as the working substance. Petrick (1993) proposed empirical relations for the production of hydrogen gases as a function of time and temperature when water is used in stainless steel heat pipe. He has inferred that continuous or repeated removal of hydrogen will stop the mid-way ceasure of the operation of heat pipe. Munzel and Krahling (1981) also worked with different grades of stainless steel and water at various operating temperatures. Feldman and Kenney (1981) has conducted lot of

12 experiments with the combination of mild steel and water. They noticed that the thermal resistance is lowered by using mild steel as the heat pipe material. However, production of noncondensable gases in their experiments is reported. Nevertheless, the performance of the heat pipe was quite satisfactory in a temperature range between 150 and 300 C. Abhat, Nguyenchi and Strel'tsov (c$ Dunn and Reay, 1980) investigated the fluid inventory on gravity assisted heat pipes. Li et al. (1993) theoretically analysed the flow and heat transfer in a wickless rotating heat pipe. Ideal charges and working conditions are also estimated from the film thickness. The effect of fluid quantity on the performance of the heat pipe was investigated Flat Heat Pipes The present work deals with flat rectangular heat pipe only. Obviously, the literature review on flat heat pipes assumes more significance. Important published articles on flat heat pipes, are detailed in this section. Comparatively, the literature on flat heat pipe is quite less. van Ooijen and Hoogendoorn (1979) have conducted an analytical study on the pressure profiles for a steady laminar incompressible two dimensional vapour flow in a flat plate heat pipe with adiabatic top plate. Continuity, Navier - Stokes and energy equations were solved for uniform evaporation and condensation rates. The stream lines, vapour velocity profiles and vapour pressure profiles were obtained at various values of the Reynolds number. They noticed reversed flow at the condenser when Re=lO and the pressure drop is more than three times that of the Poiseuille pressure when Re=50. They have also investigated experimentally (l 98 l), the vapour pressure drop and temperature profiles on a flat heat pipe with adiabatic top plate.

13 They compared the results thus obtained with the earlier results from the numerical solution. They measured the vapour pressure drop and presented the longitudinal pressure profiles in the rectang~lar vapour channel for different values of Reynolds number values. In the past few years Vafai and his colleagues have contributed noticeable results on flat heat pipe. Vafai and Wang (1992) made an in depth integral analysis revealing various physical aspects of an asymmetrical flat plate heat pipe. They presented a pseudo three dimensional vapour flow model due to asymmetrical nature of heat source and sink. The vapour velocity profiles, axial temperature variation, and pressure distribution were brought out. Vafai et al. (1995) presented the two dimensional investigation and conceptual design of a disk shaped asymmetric heat pipe. They studied the incompressible vapour flow and liquid flow in this heat pipe using conservative formulation. The vapour velocity profile, the vapour and liquid pressure distribution and vapour temperature variation obtained in asymmetric heat pipes are compared with those of rectangular heat pipes. Zhu and Vafai (1998) carried out numerical study for the steady in- compressible vapour and liquid flow in an asymmetrical flat plate heat pipe. The three dimensional model developed is extended to account for the vapour flow reversals, the liquid flow in the vertical wicks, the coupling of the liquid flow with the top and bottom wicks, the non-darcian effects of the liquid flow through the porous wick and also the gravitational effects. The velocity profiles and pressure distribution, both in vapour and liquid regimes are found to be in good agreement with the experimental results. They have developed an analytical model (1 998) for the start-up transient of asymmetrical flat plate and disk shaped heat pipes. A quasi-

14 steady state pseudo-three dimensional approximation is presented to model the heat transfer within the wall and liquid wick regions coupling with vapour phase at the vapour liquid interface. Wang and Vafai (2000) conducted experimental studies to investigate the thermal performance of a flat plat heat pipe. The temperature along the pipe wall surface is quite uniform. The results indicate that the porous wick of the evaporator section creates the main thermal resistance resulting in the largest temperature drop. This has profound effect on the performance of the heat pipe. Vafai and Wang (2000) conducted experimental studies on flat plate heat pipe to predict its performance during start up and shut down operations. They have established that the wick at the evaporator region provides the maximum resistance for heat transfer. They have also shown that the input heat has a substantial effect on the temperature increase of the heat pipe. Unnikrishnan and Sobhan (1997) obtained the transient distribution of field variables in the vapour and wick regions of a flat heat pipe. Their analysis was two dimensional employing a finite difference procedure based on SIMPLER algorithm. This numerical experimentation revealed that the wick porosity does not have a significant effect on the velocity and pressure distributions in the vapour core region. However, it is reported that the temperature distribution is slightly influenced by wick porosity. The transient model of a flat heat pipe developed by Sobhan et al. (2000) involves the solution of two dimensional continuity, momentum and energy equations coupled with equation of state in the vapour core, transport equations for the porous wick medium and two dimensional heat equation for the container wall. Using finite difference method the variation of temperature, pressure and velocity

15 fields are obtained. The effect of axial conduction through the pipe wall and wick which causes heat to flow into the interior of the externally adiabatic section, thus affecting the velocity distribution in the wick and vapour core is established. 2.3 Summary Though the conventional heat pipes are circular, flat heat pipes are also used widely for carrying large heat fluxes. It was already mentioned that most of the literature available on heat pipes are in connection with circular ones. Some important works on cylindrical heat pipe connected to the present research have been discussed. Some articles on the compatibility between the working medium with the wick and container materials are also discussed. Very less investigations have been carried out on the effect of fluid inventory in the heat pipe. A few examples of the same have been mentioned in this chapter. Some published articles on flat heat pipe have also been described briefly. Very little investigation has been carried out to study the performance of flat heat pipes, though researchers recently turned their attention to the same. The results of the literature review on heat pipes indicate the necessity and scope for further theoretical and experimental studies on flat rectangular heat pipes. The present work is an attempt to study the steady state operation of the flat rectangular heat pipes, both theoretically and experimentally. It also aims at the study of the influence of the amount of working medium and wick porosity on the performance of heat pipes.